Page:Scientific Papers of Josiah Willard Gibbs.djvu/439

This page has been proofread, but needs to be validated.

VAPOR-DENSITIES.

403

and for perchloride of phosphorus,

{\text{L}}={\frac {5441}{t_{\text{C}}+273}}+\log p-11.353.

(22)

By these equations the values of ${\text{L}}$ are easily calculated. The values of ${\text{A}}$ may then be obtained by inspection (with interpolation when necessary) of the following table. From $\Delta$ the value of ${\text{D}}$ may be obtained by multiplying by ${\text{D}}_{1}$ , viz., by 1.589 for peroxide of nitrogen or formic acid, by 2.073 for acetic acid, and by 3.6 for perchloride of phosphorus.^[1]

Table X.
For the solution of the equation: $\log {\frac {1000(\Delta -1)}{(2-\Delta )^{2}}}={\text{L}}.$
${\text{L}}$	$\Delta$	Diff.	${\text{L}}$		$\Delta$	Diff.	${\text{L}}$		$\Delta$	Diff.

.7	1.005			3.0	1.382			5.3	1.932
.8	1.006	1		3.1	1.421	39		5.4	1.939	7
.9	1.008	2		3.2	1.461	40		5.5	1.945	6
1.0	1.010	2		3.3	1.500	31		5.6	1.951	6
1.1	1.012	2		3.4	1.537	37		5.7	1.956	5
1.2	1.015	3		3.5	1.574	37		5.8	1.961	5
1.3	1.019	4		3.6	1.609	35		5.9	1.965	4
1.4	1.024	5		3.7	1.642	33		6.0	1.969	4
1.5	1.030	6		3.8	1.673	31		6.1	1.972	3
1.6	1.037	7		3.9	1.703	30		6.2	1.975	3
1.7	1.046	9		4.0	1.730	27		6.3	1.978	3
1.8	1.056	10		4.1	1.755	25		6.4	1.980	2
1.9	1.069	13		4.2	1.778	23		6.5	1.982	2
2.0	1.084	15		4.3	1.800	22		6.6	1.984	2
2.1	1.102	18		4.4	1.819	19		6.7	1.986	2
2.2	1.122	20		4.5	1.837	18		6.8	1.987	1
2.3	1.146	24		4.6	1.854	17		6.9	1.989	2
2.4	1.172	26		4.7	1.868	14		7.0	1.990	1
2.5	1.202	30		4.8	1.882	14		7.2	1.992
2.6	1.234	32		4.9	1.894	12		7.4	1.994
2.7	1.268	34		5.0	1.905	11		7.6	1.995
2.8	1.305	37		5.1	1.915	10		7.8	1.996
2.9	1.343	38		5.2	1.924	9		8.0	1.997
3.0	1.382	39		5.3	1.932	8		9.0	1.999

The constants of these equations are of course subject to correction by future experiments, which must also decide the more general question in what cases, and within what limits, and with what degree of approximation, the actual relations can be expressed by equations of such form. In the case of perchloride of phosphorus especially, the formula proposed requires confirmation.

↑ The value of $\Delta$ diminished by unity expresses the ratio of the number of the molecules of the more complex type to the whole number of molecules. Thus, if $\Delta =1.20$ , in the case of peroxide of nitrogen there are 20 molecules of the type N₂O₄ to 80 of the type NO₂, or in the case of perchloride of phosphorus there are 20 molecules of the type PCl₅ to 40 of the type PC_l3 and 40 of the type Cl₂. A consideration of the varying values of $\Delta$ is therefore more instructive than that of the values of ${\text{D}}$ , and it would in some respects be better to make the comparison of theory and experiment with respect to the values of $\Delta$ .

[1] The value of $\Delta$ diminished by unity expresses the ratio of the number of the molecules of the more complex type to the whole number of molecules. Thus, if $\Delta =1.20$ , in the case of peroxide of nitrogen there are 20 molecules of the type N₂O₄ to 80 of the type NO₂, or in the case of perchloride of phosphorus there are 20 molecules of the type PCl₅ to 40 of the type PC_l3 and 40 of the type Cl₂. A consideration of the varying values of $\Delta$ is therefore more instructive than that of the values of ${\text{D}}$ , and it would in some respects be better to make the comparison of theory and experiment with respect to the values of $\Delta$ .

[1]